Is the universe bounded or unbounded?

[otseng]

In the Light, stars, and creationism thread, I proposed a theory to reconcile a young earth with being able to see stars that are billions of light years away. The theory assumes that the Big Bang is true, however, it also assumes that the universe is bounded. In typical cosmology, it is assumed that the universe is unbounded.

Bounded means that the universe has a boundary to it. There exists an "edge" to the universe in which beyond this boundary, our universe does not exist.

In an unbounded universe, there is no "edge". The universe "wraps" around itself. So, if you are to go in any direction in a straight line, you will eventually come back to the starting point.

This is hard to conceptualize, but can be explained like a surface of a sphere. On the surface of a sphere, if you start at any point and then go in a straight line, you will eventually come back to the starting point. Now, instead a 2-D surface on a sphere, the universe is a 3-D topology that curves in on itself.

The ramifications of either of these two assumptions make for drastically different cosmological conclusions.

So, the questions are:
1. Is the universe bounded or unbounded? Why?
2. What are the ramifications of whether it is bounded or unbounded?

[Curious]

I would like to ask whether or not there is any slid evidence for a hyperuniverse. Pope Benedict has reacted rather cooly to the idea of a hyperuniverse or multiverse.

If there is a hyper-universe then it would be very doubtful that we would have any "solid" evidence for it. I suppose we could postulate that quantum mechanisms might point to the existence of such a universe as the mechanics of such appear to be inconsistent ( at least in isolation ) with our own 4-dimensional view of the universe. This might well be accounted for by our incomplete understanding of these dimensions or interactions though. It could also be postulated that the expansion of our own universe might not be an expansion "into nothingness" but a diffusion into a pre-existing hyper-universe where the original universal "seed" might incorporate the hyper-universe into its own ever growing structure. This is pure speculation, although it does overcome the problem of conservation so damaging to the present big-bang theory.

[Alien]

The reference

http://scienceworld.wolfram.com/physics/HubbleLaw.html

gives the Friedman Laimaitre model, this has been rigorously derived from General Relativity and obeys the Cosmological Principle. As I have explained with a Cosmological Principle there can be no edge, or rather no edge which is seen by any observer.

My understanding is slightly different.

The Friedman model, derived from General Relativity and scientifically verified up to now, implies that the space-time has a non-zero curvature.
Assuming that the total matter contained in the universe is finite (as far as I know, this is an assumption and cannot be demonstrated), then a curved and finite universe imply the absence of an edge.

On the other side, if you assume that the total matter of the universe is infinite, then you have also no edge.

In all cases, my understanding is that an edge cannot exist.

Independent on any Cosmological Principle, that comes on top of that.

[Ian Parker]

The Friedman model, derived from General Relativity and scientifically verified up to now, implies that the space-time has a non-zero curvature.
Assuming that the total matter contained in the universe is finite (as far as I know, this is an assumption and cannot be demonstrated), then a curved and finite universe imply the absence of an edge.

On the other side, if you assume that the total matter of the universe is infinite, then you have also no edge.

In all cases, my understanding is that an edge cannot exist.

Independent on any Cosmological Principle, that comes on top of that.

It does indeed imply non zero curvature. In fact General Relativity itself is a theory about the curvature of space. A lot depends on the value of Omega. If the Universe is open (Omega<1) the Universe's curvature does not bring it back on itself. If Omega >=1 then the Universe will be finite. It can be viewed as wrapped rund a hypersphere and expanding.

[otseng]

The Friedman model, derived from General Relativity and scientifically verified up to now, implies that the space-time has a non-zero curvature.

However, recent measurements indicate that space-time is not curved, but flat.

Boomerang backs flat universe

The geometry of the universe is Euclidean and space is flat.

Balloon-Borne Experiment Finds Evidence For A Flat Universe, Inflation And A Cosmological Constant

These results provide strong evidence that the universe is flat, with a large-scale geometry just like the Euclidean geometry everyone learns in high school.

Assuming that the total matter contained in the universe is finite (as far as I know, this is an assumption and cannot be demonstrated), then a curved and finite universe imply the absence of an edge.

I think we can safely assume that the total matter in the universe is finite. If the universe started from the singularity of the Big Bang, it could not have had infinite matter, but had some large finite amount of matter. And if the universe started off with a finite amount of matter, it could not become to have an infinite amount of matter.

If it is curved, then it would point to no edge. But if it is flat, then it would point to the universe having an edge.

In all cases, my understanding is that an edge cannot exist.

So, based on latest measurements, the evidence points to a bounded universe with an edge.

[otseng]

The “Ellis-Otseng” mathematical model does imply the existence of a geometrical centre, origin of the expansion, but this geometrical centre can be put in any place in the universe, just because we can put in any point the “zero” of our coordinate system, and the model remains consistent.

The only model where any point could be the apparent center would be a curved topology. As I've argued here, in a flat topology, the only point with an apparent center would be at (0,0,0).

But, in both options, the Ellis-Otseng model is making an act of faith because a) it fails in describing an edge b) it assumes an infinite universe (and the concept of infinite is not very scientific because it implies an infinite quantity of matter/energy in the universe).

I'm not sure what you mean by failing to describe the edge. The model simply says that an edge must exist.

Also, I do not believe the universe has an infinite amount of matter (as I have argued in the above post). Rather it must be finite. And since the universe is finite and flat, it must then have an edge.

[Ian Parker]

[ As I've argued here, in a flat topology, the only point with an apparent center would be at (0,0,0).

But, in both options, the Ellis-Otseng model is making an act of faith because a) it fails in describing an edge b) it assumes an infinite universe (and the concept of infinite is not very scientific because it implies an infinite quantity of matter/energy in the universe).

I am not sure what you mean by failing to describe the edge. The model simply says that an edge must exist.

Also, I do not believe the universe has an infinite amount of matter (as I have argued in the above post). Rather it must be finite. And since the universe is finite and flat, it must then have an edge.

It either

1) Has an edge, which is at variance with the Cosmological Principe.
2) Is closed.
3) Is infinite.

I feel I must point out the scientific consequences of option 1. If we are to meaninfully talk about 2.7K (or as someone pointed out 2.72... K) we must assume the Cosmological Principle, otherwise the fireball NEVER occurred here The same thing is true of LISA and gravitational waves. We could be too near the edge to detect cosmic gravitational waves.

As I said in earlier posings Poincaré's universe is infinite even though it does not seem to be at first sight.

[Curious]

The Friedman model, derived from General Relativity and scientifically verified up to now, implies that the space-time has a non-zero curvature.
Assuming that the total matter contained in the universe is finite (as far as I know, this is an assumption and cannot be demonstrated), then a curved and finite universe imply the absence of an edge.

On the other side, if you assume that the total matter of the universe is infinite, then you have also no edge.

In all cases, my understanding is that an edge cannot exist.

Independent on any Cosmological Principle, that comes on top of that.

It does indeed imply non zero curvature. In fact General Relativity itself is a theory about the curvature of space. A lot depends on the value of Omega. If the Universe is open (Omega<1) the Universe's curvature does not bring it back on itself. If Omega >=1 then the Universe will be finite. It can be viewed as wrapped rund a hypersphere and expanding.

Since you appear to subscribe to the theory that gravitational attraction is simply caused by spatial curvature (I may be wrong in this assumpion) I have a question concerning this.
If an object A is moving in a straight line then this "straight line" would in effect make the object head towards the large mass that causes the curvature. Now if this curvature also altered the position of the "intra spatial coordinates" this would also explain the acceleration of the object.
Now if such an object A was stationary, maintaining a fixed position in space(rather than moving in a straight line), then such a curvature caused by a nearby large mass would certainly shift the (relative) position of the original object A but what would compel such an object to continue unabated towards the large masses gravitational centre at increasing velocity?
In case anybody is wondering, this question does have some bearing on the topic at hand.

[Ian Parker]

Since you appear to subscribe to the theory that gravitational attraction is simply caused by spatial curvature (I may be wrong in this assumpion) I have a question concerning this.
If an object A is moving in a straight line then this "straight line" would in effect make the object head towards the large mass that causes the curvature. Now if this curvature also altered the position of the "intra spatial coordinates" this would also explain the acceleration of the object.
Now if such an object A was stationary, maintaining a fixed position in space(rather than moving in a straight line), then such a curvature caused by a nearby large mass would certainly shift the (relative) position of the original object A but what would compel such an object to continue unabated towards the large masses gravitational centre at increasing velocity?
In case anybody is wondering, this question does have some bearing on the topic at hand.

Yes it does indeed. This is what General Relativity is all about. Our bunch of keys falls because ds^2/dt^2 is a curvature. I don't really want to debate Relativity as such here. In Google Groups Pencho Valev insists that the theory is wrong and that muons travel not at 0.998 c or so as I state, but 150c. I have had a bellyful I have afraid. I have a web page -

http://myweb.tiscali.co.uk/ianandmargar ... tivity.htm

If anyone is interested on a similar web page you can find my wife's thesis on the Church of England

http://myweb.tiscali.co.uk/ianandmargaret/index.html

The question of curvature is pure General Relativity

[Curious]

Yes it does indeed. This is what General Relativity is all about. Our bunch of keys falls because ds^2/dt^2 is a curvature. I don't really want to debate Relativity as such here. In Google Groups Pencho Valev insists that the theory is wrong and that muons travel not at 0.998 c or so as I state, but 150c. I have had a bellyful I have afraid. I have a web page -

http://myweb.tiscali.co.uk/ianandmargar ... tivity.htm

If anyone is interested on a similar web page you can find my wife's thesis on the Church of England

http://myweb.tiscali.co.uk/ianandmargaret/index.html

The question of curvature is pure General Relativity

I quite understand your wish not to get into the intricacies of such a debate. My question really was meant as a rhetorical aside, aimed more towards getting people to consider the problem than to provoke an actual literary response. I do find however it far more illuminating and infinitely more interesting to hear the views of those unencumbered by scientific "fact" and the conclusions of others.

[Alien]

I am very reluctant to accept singularities.

About critical density:
How can we be so sure to say that the universe is flat and its density has EXACTLY the critical value? This value is a borderline, a theoretical boundary that discriminates exactly two behaviours. It's more a philosophical boundary than a really suitable possibility. The value of this boundary has to be exactly defined or measured. Mathematically, a fraction of 10E-100 or even less, would influence the final destiny of the universe! A single electron more or less in a cubic inch would make the difference! Why should the universe possess an exact value that is only mathematically defined?
As we have already seen examples by which a measurement can never be 100% accurate, and Nature shows us inaccurate phenomena, I would not agree with the absolute statement that "the universe is flat". We can discuss whether it is open or closed, and whether a certain consideration or measurement tends toward one direction or the other, but it would be impossible to claim that the density of the universe is EXACTLY the critical value.
The measurements from Boomerang quoted by Otseng are just in the direction of a "flatter" universe, ie a universe that is less "open" as it would seem.

About the edge:
Similarly, I would not use the concept of "edge", because this implies a lot of complications (what is behind the edge?). An edge would pretend to be defined. Are we saying that beyond what we call an "edge" there is another universe? What would define if you are on one side or the other? Would the edge be part of this universe or the other? If of none, then it would not be an edge!

About the infinite:
The concept of "infinite" gives us sufficient troubles in mathematics (paradoxes and similar) that I would avoid it in physics.
The universe might be infinite only in one sense: it contains an infinite quantity of matter in an infinite dimension.
An infinite quantity of matter in a finite dimension would give an infinite averaged density, and an infinite density would not match with an expanding universe.
A finite quantity of matter in an infinite dimension would give us a problem that is non-solvable. Going far away, the matter would disappear (because the dimension is infinite but the matter is finite). And, if matter disappears, then it is a nonsense to talk about a space. How can you define an infinite space without a single electron in it? A dimension can only make sense if there is another second reference piece of matter that gives you a distance.

Having rejected, for simplicity, the three boundaries/singularities called "exactness", "edge" and "infinite", I would only leave the following options:

#1
the universe is "closed", ie homogeneous, with spherical curvature, unbounded, with finite matter, simply connected, and will reverse its expansion
#2
the universe is "open", ie homogeneous, with hyperbolic curvature, unbounded, with finite matter, non-simply connected, and will continue its expansion for ever
#3
the universe is non-homogeneous, with different local curvatures, unbounded, with finite matter, non-simply connected, and will evolve into a sort of fractal, breaking into individual universes, some expanding and some crunching (effectively, we could be living in one of the individual universes generated by fractioning a previous universe...)